FLOWING: Implicit Neural Flows for Structure-Preserving Morphing

Arthur Bizzi (EPFL - EPF Lausanne) · Matias Grynberg Portnoy (Universidad de Buenos Aires) · Vitor Pereira Matias (Universidade de São Paulo - USP - ICMC) · Daniel Perazzo (IMPA) · João Paulo Silva do Monte Lima (Universidade Federal Rural de Pernambuco) · Luiz Velho (IMPA) · Nuno Gonçalves (University of Coimbra) · João Pereira (University of Georgia) · Guilherme Schardong (Institute of Systems and Robotics, University of Coimbra) · Tiago Novello (IMPA)

2d images3d shapesconvergencedifferential vector flowfeature alignment gaussian splatting implicit neural representations interpolationmeshlessnessmorphingmultilayer perceptronsregularizationsstable transformationsstructural flow propertiestemporal coherence

Morphing is a long-standing problem in vision and computer graphics, requir- ing a time-dependent warping for feature alignment and a blending for smooth interpolation. Recently, multilayer perceptrons (MLPs) have been explored as implicit neural representations (INRs) for modeling such deformations, due to their meshlessness and differentiability; however, extracting coherent and accurate morphings from standard MLPs typically relies on costly regularizations, which often lead to unstable training and prevent effective feature alignment. To overcome these limitations, we propose FLOWING (FLOW morphING), a framework that recasts warping as the construction of a differential vector flow, naturally ensuring continuity, invertibility, and temporal coherence by encoding structural flow prop- erties directly into the network architectures. This flow-centric approach yields principled and stable transformations, enabling accurate and structure-preserving morphing of both 2D images and 3D shapes. Extensive experiments across a range of applications—including face and image morphing, as well as Gaussian Splatting morphing—show that FLOWING achieves state-of-the-art morphing quality with faster convergence. Code and pretrained models are available in https://schardong.github.io/flowing.